Hilbert's third problem and a conjecture of Goncharov

Abstract

In this paper we reduce the generalized Hilbert's third problem about Dehn invariants and scissors congruence classes to the injectivity of certain Chern--Simons invariants. We also establish a version of a conjecture of Goncharov relating scissors congruence groups of polytopes and the algebraic $K$-theory of $\mathbf{C}$.

arXiv commentCurrent version is slightly different from previous: the maps relating K-theory and the Goncharov complex go in the other direction